Complex amplitude modulation by use of liquid-crystal spatial light modulators

Predictive search algorithm for phase holography

We present an algorithm for generating high-quality holograms for computer generated holography: holographic predictive search. This approach is presented as an alternative to traditional holographic search algorithms such as direct search (DS) and simulated annealing (SA). We first introduce the current search-based methods and then introduce an analytical model of the underlying Fourier elements. This is used to make prescient judgments regarding the next iteration of the algorithm. This approach is developed for the case of phase-modulating devices with phase-sensitive reconstructions. When compared to conventional iterative approaches such as DS and SA on a multiphase device, holographic predictive search offered a fivefold improvement in quality as well as up to a 10-fold improvement in convergence time. This comes at the cost of an increased iteration overhead.

Improving holographic search algorithms using sorted pixel selection

Traditional search algorithms for computer hologram generation such as Direct Search and Simulated Annealing offer some of the best hologram qualities at convergence when compared to rival approaches. Their slow generation times and high processing power requirements mean, however, that they see little use in performance critical applications. This paper presents the novel sorted pixel selection (SPS) modification for holographic search algorithms that offers mean square error reductions in the range of 14.7-19.2% for the test images used. SPS operates by substituting a weighted search selection procedure for traditional random pixel selection processes. While small, the improvements seen are observed consistently across a wide range of test cases and require limited overhead for implementation.

Phase flicker optimisation in digital liquid crystal on silicon devices

Phase flickers in the digital liquid crystal on silicon (LCOS) devices employing the pulse width modulation (PWM) driving scheme have a detrimental effect on optical performances, especially in the non-display applications. This paper investigated the relationship between the PWM waveform and the corresponding phase flicker in digital LCOS devices. It has been identified that the magnitude of the phase flicker depends on the pulse patterns in the driving waveform as well as the dynamic response of the liquid crystal molecules at different tilting angles. A simple but generic method has been developed based on these findings, which is able to accurately predict the temporal phase response of the liquid crystal to any PWM waveforms. This method is further used for rapid identifications of low-flicker PWM waveforms, without the need for increasing the complexity of the driving circuitry. The peak-to-peak phase flicker in the LCOS device under our investigation has been reduced by >80% from ∼0.16pi to ∼0.03pi when operating at 30°C.

Complete amplitude and phase control of light using broadband holographic metasurfaces

Reconstruction of light profiles with amplitude and phase information, called holography, is an attractive optical technology with various significant applications such as three-dimensional imaging and optical data storage. Subwavelength spatial control of both amplitude and phase of light is an essential requirement for an ideal hologram. However, traditional holographic devices suffer from their restricted capabilities of incomplete modulation in both amplitude and phase of visible light; this results in sacrifice of optical information and undesirable occurrences of critical noises in holographic images. Herein, we have proposed a novel metasurface that is capable of completely controlling both the amplitude and phase profiles of visible light independently with subwavelength spatial resolution. The full, continuous, and broadband control of both amplitude and phase was achieved using X-shaped meta-atoms based on the expanded concept of the Pancharatnam-Berry phase. The first experimental demonstrations of the complete complex-amplitude holograms with subwavelength definition at visible wavelengths were achieved, and excellent performances with a remarkable signal-to-noise ratio as compared to those of traditional phase-only holograms were obtained. Extraordinary control capability with versatile advantages of our metasurface paves a way to an ideal holography, which is expected to be a significant advancement in the field of optical holography and metasurfaces.

Color dynamic holographic display with wide viewing angle by improved complex amplitude modulation

An improved method of complex amplitude modulation (CAM) is proposed for color holographic display with a wide viewing angle. Bandlimited random initial phase is introduced to the CAM method, which overcomes the drawbacks brought by a constant initial phase and maintains the advantages of CAM. Modifications in CAM for color display are also explained. Both simulation and experimental results verify that the proposed method can reconstruct color 3D scenes successfully without the time-consuming process for encoding the computer-generated holograms. Compared with the display via traditional CAM, the results exhibit that the proposed method can reconstruct color 3D scenes with a better viewing effect. Because of the display effect improvement and the high calculation speed, this method can be applied to high performance holographic display.

Flattening axial intensity oscillations of a diffracted Bessel beam through a cardioid-like hole

We present a new feasible way to flatten the axial intensity oscillations for diffraction of a finite-sized Bessel beam, through designing a cardioid-like hole. The boundary formula of the cardioid-like hole is given analytically. Numerical results by the complete Rayleigh-Sommerfeld method reveal that the Bessel beam propagates stably in a considerably long axial range, after passing through the cardioid-like hole. Compared with the gradually absorbing apodization technique in previous papers, in this paper a hard truncation of the incident Bessel beam is employed at the cardioid-like hole edges. The proposed hard apodization technique takes two advantages in suppressing the axial intensity oscillations, i.e., easier implementation and higher accuracy. It is expected to have practical applications in laser machining, light sectioning, or optical trapping.

3D dynamic holographic display by modulating complex amplitude experimentally

Complex amplitude modulation method is presented theoretically and performed experimentally for three-dimensional (3D) dynamic holographic display with reduced speckle using a single phase-only spatial light modulator. The determination of essential factors is discussed based on the basic principle and theory. The numerical simulations and optical experiments are performed, where the static and animated objects without refinement on the surfaces and without random initial phases are reconstructed successfully. The results indicate that this method can reduce the speckle in reconstructed images effectively; furthermore, it will not cause the internal structure in the reconstructed pixels. Since the complex amplitude modulation is based on the principle of phase-only hologram, it does not need the stringent alignment of pixels. This method can be used for high resolution imaging or measurement in various optical areas.

Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation

A method to measure the optical response across the surface of a phase-only liquid crystal on silicon device using binary phase gratings is described together with a procedure to compensate its spatial optical phase variation. As a result, the residual power between zero and the minima of the first diffraction order for a binary grating can be reduced by more than 10 dB, from -15.98 dB to -26.29 dB. This phase compensation method is also shown to be useful in nonbinary cases. A reduction in the worst crosstalk by 5.32 dB can be achieved when quantized blazed gratings are used.

Extended phase modulation depth in twisted nematic liquid crystal displays

We show how the phase modulation depth in twisted nematic liquid crystal displays (TNLCDs) can be increased dramatically by selecting a polarization configuration with a reduced mean intensity transmission. This phenomenon, which we have validated with various devices, is shown here for a device that presents a phase-only modulation only slightly over π radians in our classical rotated eigenvector configuration, but it is capable of producing close to a 2π phase depth for a configuration with 5% mean intensity transmission. A quantitative explanation is presented by means of a phasor analysis of the TNLCD eigenvector projections over input and output polarization states. The proposed technique can be a very useful solution in modern TNLCDs that have a very thin liquid crystal layer and a reduced maximum achievable phase modulation.

Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude, and phase diffraction gratings

We analyze the performance of a ferroelectric liquid crystal on silicon display (FLCoS) as a binary polarization diffraction grating. We analyze the correspondence between the two polarization states emerging from the displayed grating and the polarization and intensity of the diffracted orders generated at the Fourier diffraction plane. This polarization-diffraction analysis leads, in a simple manner, to configurations yielding binary amplitude or binary phase modulation by incorporating an analyzer on the reflected beam. Based on this analysis, we present two useful variations of the polarization configuration. The first is a simplification using a single polarizer, which provides equivalent results for amplitude or phase modulation as the more general operational mode involving two polarizers. The second variation is proposed to compensate the reduction of the diffraction efficiency when the operating wavelength differs from the design one (for which the FLCoS liquid-crystal layer acts as a half-wave plate). In this situation we show how the ideal grating performance can be recovered in spite of the phase-shift mismatch originated by chromatic dispersion. In all cases, we provide experimental results that verify the theoretical analyses.

Phase calibration of spatially nonuniform spatial light modulators

A new 512 x 512 pixel phase-only spatial light modulator (SLM) has been found to deviate from being flat by several wavelengths. Also, the retardation of the SLM relative to voltage varies across the device by as much as 0.25 wavelength. The birefringence of each pixel as a function of address voltage is measured from the intensity of the SLM between crossed polarizers. To these responses are added a reference spatial phase measured by phase shifting interferometry for a single address voltage. Fits to the measured data facilitate the compensation of the SLM to a root-mean-square wave-front error of 0.06 wavelength. The application of these corrections to flatten the full aperture of the SLM sharpens the focal plane spot and reduces the distortion of computer-designed diffraction patterns.

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.

Hyperresolving phase-only filters with an optically addressable liquid crystal spatial light modulator

Hyperresolving (sometimes called 'superresolving' or 'ultraresolving') phase-only filters can be generated using an optically addressable liquid crystal spatial light modulator. This approach avoids the problems of low efficiency, and coupling between amplitude and phase modulation, that arise when using conventional liquid crystal modulators. When addressed by a programmed light intensity distribution, it allows filters to be changed rapidly to modify the response of a system or permit the investigation of different filter designs. In this paper we present experimental hyperresolved images obtained using an optically addressable parallel-aligned nematic LCD with two zone Toraldo type phase-only filters. The images are compared with theoretical predictions.

Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays

We present a general formulation based on the Jones-matrix theory for reciprocal nonabsorbing polarization devices, including polarization interference filters and liquid-crystal displays. The development of this formulation is based on general symmetry conditions that relate the Jones matrix when the device is illuminated from the front side and from the back side. The application to liquid-crystal displays results in a constraint of the Jones-matrix elements, which represents a generalization of the existing models that explain their modulation properties.

Optical implementation of segmented composite filtering

We investigate possible performance improvements of coherent optical correlators by using an appropriate filter design. Multidecision strategies are often required in high-level image-processing tasks. For an optical system characterized by a given space-bandwidth product we show that the filter design plays a crucial role in satisfying both system and processing requirements, with respect to the optimization of the encoding capacity. This leads us to the definition of segmented composite filtering, which is discussed in terms of processing performance. This filtering is assessed experimentally in the case of a face-recognition problem.

Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator

An improved method for implementing correlation filters in the joint transform correlator architecture is proposed. We derived the method from computer-generated holography techniques. It allows us to use any correlation filters, especially ones that provide an optimal trade-off between noise robustness, peak sharpness, and optical efficiency, with any spatial light modulator (SLM). This method also allows for an objective comparison of the performance of the coding domains of various SLM's.

Reconfigurable two-dimensional diffractive phase element with the fractional talbot effect

We investigate the technical feasibility of the optical implementation of a four-phase-level diffractive element with two {0, pi}-phase spatial light modulators in a fractional Talbot configuration. The space-bandwidth product of the spatial light modulators is seen as the main theoretical limitation of the proposed approach. We investigate the robustness of technological and geometrical parameters on the diffraction efficiency of the whole system. Ferroelectric liquid-crystal silicon backplane spatial light modulators are chosen because of their high reconfiguration rates and good electro-optics interface. Similarly, we assess the influence of liquid-crystal technical parameters on system performance.

Characteristics of a 128 x 128 liquid-crystal spatial light modulator for wave-front generation

Spatial and temporal characteristics of a 128x128 zero-twist nematic liquid-crystal spatial light modulator are investigated for wave-front generation at a wavelength of 632.8 nm. The modulator is found to have the capability of producing at least eight phase levels between 0 and 2pi , and the rate of arbitrary phase modulation is limited to approximately 4.5 Hz. Wave-front generation of the first 55 Zernike polynomials is demonstrated.

Performance comparison of ferroelectric liquid-crystal-technology-based coherent optical multichannel correlators

Our purpose is to compare two architectures when implemented with ferroelectric liquid-crystal technology: the conventional VanderLugt and joint transform correlators. The architectures are compared in the single-correlation and multichannel cases. The analysis covers both theoretical aspects and practical considerations regarding implementation. Specifications for a multichannel correlator design, including considerations of both spatial light modulators and architecture configurations, are discussed. Experimental results are presented for both architectures. Finally, the benefit resulting from extension to multichannel operation is discussed in terms of both multiplexing and algorithmic capabilities.